5 citations · 11 across the 9 of their papers we have counts for
10 papers
Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces
Luca Capogna, Ryan Gibara, Riikka Korte +1
We prove global Hölder regularity result for weak solutions to a PDE of -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…
Fractional -Laplacians via Neumann problems in unbounded metric measure spaces
Luca Capogna, Ryan Gibara, Riikka Korte +1
We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional -Laplace non-homogeneous equation , with , , for d…
On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry
Ryan Gibara, Ilmari Kangasniemi, Nageswari Shanmugalingam
We study the large-scale behavior of Newton-Sobolev functions on complete, connected, proper, separable metric measure spaces equipped with a Borel measure with …
On the Dirichlet-to-Neumann Map for the -Laplacian on a Metric Measure Space
Ryan Gibara, Nageswari Shanmugalingam
In this note, we construct a Dirichlet-to-Neumann map, from a Besov space of functions, to the dual of this class. The Besov spaces are of functions on the boundary of a bounded, l…
Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equ…
Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a -Poincaré inequality
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…
Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces
Ryan Gibara, Nageswari Shanmugalingam
In this paper we fix and consider $(\Om,d,μ)$ be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure supporting a…
Solving a Dirichlet problem for unbounded domains via a conformal transformation
Ryan Gibara, Riikka Korte, Nageswari Shanmugalingam
In this paper, we solve the -Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure s…
Conformal transformation of uniform domains under weights that depend on distance to the boundary
Ryan Gibara, Nageswari Shanmugalingam
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected…
Accessible parts of the boundary for domains in metric measure spaces
Ryan Gibara, Riikka Korte
We prove in the setting of --Ahlfors regular PI--spaces the following result: if a domain has uniformly large boundary when measured with respect to the --dimensional Hausdor…